Passengers who were unable to fly last weekend are eligible for a free return economy flight within Australia or to New Zealand, the company said in a statement Sunday.
The initiative will cost the airline about A$20 million, ($20.73 million), a spokeswoman confirmed.
Qantas grounded its fleet in order to force a resolution to an ongoing dispute with trade unions over pay, conditions and job security.
The shutdown stranded tens of thousands of passengers and angered the federal government, which intervened and sent the dispute to the workplace umpire, FairWork Australia, which then ordered an end to the industrial action.
"Throughout the long period of industrial activity we have been acutely aware of the impact on our customers," chief executive Alan Joyce said.
"This ticket offer is one of a range of initiatives we will be launching as a way of saying sorry as we move forward into this period of stability."The airline said it will make further announcements shortly in relation to customers based outside Australia and for members of its frequent flyer program.